Sides are added to a convex polygon so that the sum of its interior angle measures is increased by 540 degrees. How many sides are added to the polygon?

Question

anonymous · Answer

Let n be the number of sides of the original conves ploygon, The sum of the interior angles is (n-2)180.

 If we increase the number of sides by x sides, then the sum of the interior angles will become (n+x-2) 180. 

Use what you have as hypothesis to write an equation in x and solve for x.

directrix · Answer

540/180 = 3 sides

From above, (n+x-2) 180 indicates the sum of the angles of the expanded polygon.

(n+x-2) 180 = 180 (n-2) + 180 x
180x = 540
x = 3 additional sides